Strong law of large numbers for a class of superdiffusions

Rong Li Liu, Yan Xia Ren, Renming Song

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we prove that, under certain conditions, a strong law of large numbers holds for a class of superdiffusions X corresponding to the evolution equation ∂ t u t =Lu t +βu t -ψ(u t ) on a domain of finite Lebesgue measure in R d, where L is the generator of the underlying diffusion and the branching mechanism ψ(x,λ)= 1/2α(x) λ2+∫0∞(e-λr- 1+λr)n(x, dr) satisfies supx∈D0 (r r2) n(x, dr)<∞.

Original languageEnglish (US)
Pages (from-to)73-97
Number of pages25
JournalActa Applicandae Mathematicae
Volume123
Issue number1
DOIs
StatePublished - Feb 2013

Keywords

  • Martingale
  • Point process
  • Principal eigenvalue
  • Strong law of large numbers
  • Superdiffusion

ASJC Scopus subject areas

  • Applied Mathematics

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